The New Sudoku Players' Forum

[oneshot]

Well, it's only 4X4, and she can get started on 6X6...
Anyway, does anyone know where I can get more 4X4's or 6X6's because the book she has is almost finished.
Or maybe a generator I can set to 4X4?

Thanks in advance!

Brian

[evert]

With a killer sudoku solver, if it allows you to configure the killer groups, this is how you could have it generate a 4x4 sudoku.

- within r1-4c1-4: configure each row, column and 2x2 box as a group with killer total 10
- configure no other groups
- generate a puzzle

Then r1-4c1-4 should contain a valid 4x4 sudoku, and all outside this area can be ignored.

[ronk]

... does anyone know where I can get more 4X4's or 6X6's because the book she has is almost finished.

There are many hits returned by a Google search on "4x4 sudoku puzzles kids". You should be able to find something suitable after clicking here.

[JPF]

There are only 36 different (minimal) 4x4 puzzles.

The complete list is given here

Here is the list of all the 4 clue puzzles; probably the most challenging for a young kid:

Code: Select all

. . | . .
. . | . 1
----+----
. 1 | . 2
3 . | . .

Code: Select all

. . | . .
. . | . 1
----+----
. 1 | 2 .
. 3 | . .

Code: Select all

. . | . .
. . | . 1
----+----
. 2 | . .
. 3 | . 4


Code: Select all

. . | . .
. . | . 1
----+----
. 2 | . .
. 3 | 2 .


Code: Select all

. . | . .
. . | . 1
----+----
. 2 | . .
3 . | 4 .


Code: Select all

. . | . .
. . | 1 2
----+----
. . | . .
1 3 | . .


Code: Select all

. . | . .
. 1 | . 2
----+----
. . | . .
. 3 | 4 .


Code: Select all

. . | . .
. 1 | . 2
----+----
. . | . .
1 . | 3 .


Code: Select all

. . | . .
. 1 | . 2
----+----
. . | . .
2 . | 3 .


Code: Select all

. . | . .
. 1 | . 2
----+----
. . | . .
3 . | 4 .


Code: Select all

. . | . .
. 1 | . 2
----+----
. . | 3 .
4 . | . .


Code: Select all

. . | . 1
. 1 | . .
----+----
. . | 2 .
3 . | . .


Code: Select all

. . | . 1
. 2 | . .
----+----
. . | 3 .
4 . | . .


The maximum number of clues for a minimal puzzle is 6.

Here are example of minimal puzzles with 5 and 6 clues :

Code: Select all

1 2 | 3 .
. . | . .
----+----
. . | . .
. 3 | 2 .


Code: Select all

1 2 | . .
. . | . .
----+----
2 . | . 3
. 3 | . 1


JPF

[Pat]

she can get started on 6X6...

does anyone know where I can get 6X6s

menneske 2x3

[oneshot]

Thanks everyone! She's loving it!

[Tomoka]

There are only 36 different (minimal) 4x4 puzzles.
...
Here is the list of all the 4 clue puzzles; probably the most challenging for a young kid:
...
The maximum number of clues for a minimal puzzle is 6.

Here are example of minimal puzzles with 5 and 6 clues :
...
JPF

The number "36 minimal puzzles" doesn't seem to match the result of 288 which is provided here:
http://forum.enjoysudoku.com/sudoku-maths-can-mortals-work-it-out-for-the-2x2-square-t170.html#p2992
Are some of the 288 puzzles equivalent to each other? Or are some non-minimal?

[StrmCkr]

288, different Unique solution

necro'd a very old topic, but for sporting fun.

Serg replied better

[Tomoka]

"288 unique solutions" means "288 minimal non-equivalent Sudokus"?

If this is established as correct, then the info in this thread There are only 36 different (minimal) 4x4 puzzles is not correct.

It's surprising that info about a small and comparatively easy-to-evaluate Sudoku was on this thread for so long and never corrected.

[StrmCkr]

Deleted, ser has better explination

[Tomoka]

Post #4 (of August 17, 2012) says "There are only 36 different (minimal) 4x4 puzzles" then gives examples of minimal puzzles with 4, 5 and 6 clues.

Your info says "There are 36 ways to place 4 digits...which yields one solution."

If there are minimal puzzles with 5 clues, and 6 clues, then the number of puzzles must include the set of your puzzles, plus others, yielding a total of more than 36.

Thus, the number of non-equivalent minimal 4x4 Sudokus remains either unresolved, or answered with ambiguous and/or contradictory statements.

[Serg]

Hi, Tomoka!

Post #4 (of August 17, 2012) says "There are only 36 different (minimal) 4x4 puzzles" then gives examples of minimal puzzles with 4, 5 and 6 clues.

Your info says "There are 36 ways to place 4 digits...which yields one solution."

If there are minimal puzzles with 5 clues, and 6 clues, then the number of puzzles must include the set of your puzzles, plus others, yielding a total of more than 36.

Thus, the number of non-equivalent minimal 4x4 Sudokus remains either unresolved, or answered with ambiguous and/or contradictory statements.

4x4 puzzles are known as "shidoku" (or "Shi Doku"). Here is a link to Sudopedia page, describing properties of shidoku puzzles: http://sudopedia.enjoysudoku.com/Shi_Doku.html.

I can briefly answer your questions. There are 36 essentially different minimal valid shidoku (4x4 Sudoku) puzzles. 13 of which contain 4 clues (all 13 puzzles posted in this thread by JPF). 22 minimal valid shidoku puzzles contain 5 clues and 1 minimal valid shidoku puzzle contains 6 clues.

Serg

[Tomoka]

Thanks Serg and StrmCkr. That answers my question perfectly. I think the shidoku with 6 clues is most interesting in that it is the only Sudoku of the form n^2 x n^2 where it is known with certainty that one (and only one) such example exists.

Btw, I'll try not to necropost too often (a word I learned from StrmCkr) unless I really think the topic really needs more attention.

[gamelover]

Your kid is really amazing. Sudoku is definitely a great game for kids. Here is a list of free puzzle games https://games.lol/puzzle/ Hope your kid will like it.